The triple-digit rise in the Dow continues a bout of market volatility caused by investors and traders who are worried about the Fed ending its economic stimulus. Last Wednesday, Fed Chairman Ben Bernanke said he expects the Fed to end its bond buying by the middle of 2014 if it feels the economy can manage without that stimulus.

The Dow then plunged by triple digits on three of the next four trading days, with investors worried that the market would struggle without the Fed propping it up.

Some investors concluded that the recent sell-offs were overblown.

"This is the day where the dust appears to be settling," said Jonathan Lewis, chief investment officer at Samson Capital Advisors in New York.

Quincy Krosby, a market strategist at Prudential Financial, guessed that shorter-term traders bought stocks Tuesday because they judged that parts of the market were "oversold.

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Among the biggest gainers were big dividend payers like phone and power companies. These are stocks that have been hit the hardest by the recent sell-off.

Long-term investors were likely still sitting on the sidelines, waiting for further signs that markets are becoming less volatile, Krosby said.

The stronger economic news for the U.S. led investors to sell U.S. government bonds, a sign that they're more comfortable putting money in stocks. The yield on the 10-year Treasury note, a benchmark for many types of loans, rose to 2.6 percent from 2.54 percent late Monday.

The big economic reports Tuesday revealed.

—Orders for durable goods rose 3.6 percent in May, matching April's gain. The gauge is important because U.S. manufacturing has generally struggled this year as demand for American exports slows in other parts of the world.

— U.S. home prices jumped 12.1 percent in April compared with a year ago, according to the Standard & Poor's/Case-Shiller 20-city home price index. That was the biggest year-over-year gain since March 2006. For a fourth straight month, prices rose from a year earlier in all 20 cities in the index. Twelve cities posted double-digit price gains.

— The Conference Board's consumer confidence index jumped to 81.4 in June, the best reading since January 2008. The May reading, however, was revised down to 74.3 from the original estimate of 76.2.

— Sales of new homes rose in May to a seasonally adjusted annual rate of 476,000, the Commerce Department said. That was the fastest pace since July 2008. Though sales of new homes remain below the 700,000 annual rate that most economists consider healthy, the pace has jumped 29 percent from a year ago.

Chris Baggini, senior portfolio manager at Turner Investments in Berwyn, Penn., said investors had used Bernanke's statements last week as an excuse to get out of the market—something they wanted to do anyway, given its steady run-up for most of the year.

The S&P 500 is up 11 percent for the year. But at its peak last month, it was up 17 percent.

—Barnes & Noble plunged after reporting a loss that more than doubled in the latest quarter. The bookseller struggled to compete with online retailers and its Nook e-book continued to lose money. The stock fell $3.21, or more than 17 percent, to $15.61.

—Clothing chain Men's Wearhouse rose after saying it had fired executive chairman George Zimmer, the company's founder and star of its TV commercials, because he had advocated for "significant changes that would enable him to regain control," according to the company. The stock rose $2, or nearly 6 percent, to $37.13.